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CMMSE: Maximal regularity and two-sided estimates of the approximation numbers of the nonlinear Sturm-Liouville equation solutions with rapidly oscillating coefficients in $L_{2} (R)$
  • Madi Muratbekov,
  • Mussakan Muratbekov,
  • Serik Altynbek
Madi Muratbekov
Kazakh University of Economics Finance and International Trade

Corresponding Author:[email protected]

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Mussakan Muratbekov
Taraz State University named after M Kh Dulaty
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Serik Altynbek
Esil University
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Abstract

A theorem on the maximum regularity of solutions of the nonlinear Sturm-Liouville equation with greatly growing and rapidly oscillating potential in the space $L_2(R)\,(R=(-\infty,\infty))$ is proved in this paper. Two-sided estimates of the Kolmogorov widths of the sets associated with solutions of the nonlinear Sturm-Liouville equation are also obtained. As is known, the obtained estimates given the opportunity to choose approximation apparatus that guarantees the maximum possible error.
24 Aug 2022Submitted to Mathematical Methods in the Applied Sciences
25 Aug 2022Submission Checks Completed
25 Aug 2022Assigned to Editor
26 Aug 2022Review(s) Completed, Editorial Evaluation Pending
27 Aug 2022Editorial Decision: Revise Major
02 Sep 20221st Revision Received
05 Sep 2022Submission Checks Completed
05 Sep 2022Assigned to Editor
05 Sep 2022Reviewer(s) Assigned
29 Sep 2022Review(s) Completed, Editorial Evaluation Pending
27 Dec 2022Editorial Decision: Revise Minor
30 Dec 20222nd Revision Received
31 Dec 2022Submission Checks Completed
31 Dec 2022Assigned to Editor
31 Dec 2022Review(s) Completed, Editorial Evaluation Pending
31 Dec 2022Reviewer(s) Assigned
24 Feb 2023Editorial Decision: Revise Major
13 Mar 20233rd Revision Received
14 Mar 2023Submission Checks Completed
14 Mar 2023Assigned to Editor
14 Mar 2023Review(s) Completed, Editorial Evaluation Pending
20 Mar 2023Reviewer(s) Assigned
27 Mar 2023Editorial Decision: Accept